The effects of a unilateral cut in emissions (e.g., by Annexure 1 countries in Kyoto) are analysed in a dynamic two-country two-commodity model. If the fossil fuel is priced at marginal cost, then a unilateral cut reduces total emissions (the carbon leakage is less than 100%). But if the fuel is priced above marginal cost, then a ‘green paradox’ appears, that is, the price of the fuel will fall until its use (over time) exhausts the entire stock. Here, a unilateral policy is self-defeating and it is necessary to get binding commitments on fossil fuel use from all the countries. The production and trade implications for the participant and non-participant countries are analysed. JEL: Q4, Q50, Q54, Q56